reserve G for _Graph;

theorem Th9:
  G is loopfull iff VertexDomRel(G) is total reflexive
proof
  hereby
    assume G is loopfull;
    then id the_Vertices_of G c= VertexDomRel(G) by Lm2;
    hence VertexDomRel(G) is total reflexive by ROUGHS_1:3;
  end;
  assume VertexDomRel(G) is total reflexive;
  then id the_Vertices_of G c= VertexDomRel(G) by ROUGHS_1:3;
  hence G is loopfull by Lm2;
end;
